Phenomenology of aging in the Kardar-Parisi-Zhang equation

Henkel, Malte; Noh, Jae Dong; Pleimling, Michel

doi:10.1103/physreve.85.030102

Cited by 50 publications

(91 citation statements)

References 49 publications

(57 reference statements)

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“…Adapting a protocol discussed in Ref. [44], one can consider a space-dependent rate where q x = q 0 ± a x ε is the rate at position x. Here, a x = ±1, whereas ε is a small parameter.…”

Section: Different Responsesmentioning

confidence: 99%

Aging processes in systems with anomalous slow dynamics

Afzal

Pleimling²

2013

Phys. Rev. E

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Recently, different numerical studies of coarsening in disordered systems have shown the existence of a crossover from an initial, transient, power-law domain growth to a slower, presumably logarithmic, growth. However, due to the very slow dynamics and the long-lasting transient regime, one is usually not able to fully enter the asymptotic regime when investigating the relaxation of these systems toward equilibrium. We here study two simple driven systems-the one-dimensional ABC model and a related domain model with simplified dynamicsthat are known to exhibit anomalous slow relaxation where the asymptotic logarithmic growth regime is readily accessible. Studying two-times correlation and response functions, we focus on aging processes and dynamical scaling during logarithmic growth. Using the time-dependent growth length as the scaling variable, a simple aging picture emerges that is expected to also prevail in the asymptotic regime of disordered ferromagnets and spin glasses.

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“…Adapting a protocol discussed in Ref. [44], one can consider a space-dependent rate where q x = q 0 ± a x ε is the rate at position x. Here, a x = ±1, whereas ε is a small parameter.…”

Section: Different Responsesmentioning

confidence: 99%

Aging processes in systems with anomalous slow dynamics

Afzal

Pleimling²

2013

Phys. Rev. E

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“…It is now well-established that they both undergo ageing in the sense that the three defining properties listed in the introduction are satisfied, see e.g. [62,22,24,92,21,48,56].…”

Section: Applicationsmentioning

confidence: 99%

“…In figure 3a, the simulational data from [48] are compared with the predicted form (6.5). Very large values of the waiting time s are required, and one may observe from figure 3a that even data with s < 10 3 are not yet fully in the scaling regime.…”

Section: One-dimensional Kardar-parisi-zhang Equationmentioning

confidence: 99%

“…Following [48], in order to compare the data in figure 3a with the prediction (5.6) (with the tacit extension to generic z mentioned above), we first make the working hypothesis that R(t, s) = ψ(t) ψ(s) , where the two scaling operators ψ and ψ are described by the logarithmically extended scaling dimensions…”

Section: One-dimensional Kardar-parisi-zhang Equationmentioning

confidence: 99%

“…together with the generalised Family-Vicsek scaling [62,12,18,21,67,48]. The autoresponse exponent is read off from f χ (y) ∼ y −λ R /z for y → ∞.…”

Section: One-dimensional Kardar-parisi-zhang Equationmentioning

confidence: 99%

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Logarithmic correlators or responses in non-relativistic analogues of conformal invariance

Henkel¹,

Rouhani²

2013

J. Phys. A: Math. Theor.

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Recent developments on emergence of logarithmic terms in correlators or response functions of models which exhibit dynamical symmetries analogous to conformal invariance in not necessarily relativistic systems are reviewed. The main examples of these are logarithmic Schrödinger-invariance and logarithmic conformal Galilean invariance. Some applications of these ideas to statistical physics are described.

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Algebra, Geometry and Mathematical Physics

Henkel

2014

Springer Proceedings in Mathematics &Amp; Statistics

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Phenomenology of aging in the Kardar-Parisi-Zhang equation

Cited by 50 publications

References 49 publications

Aging processes in systems with anomalous slow dynamics

Aging processes in systems with anomalous slow dynamics

Logarithmic correlators or responses in non-relativistic analogues of conformal invariance

Algebra, Geometry and Mathematical Physics

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